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Hopf Bifurcation in A New Chaotic System via Hybrid Control Strategy
Fatin Najwa Binti Rahim
Supervisor: Assoc. Prof. Dr. Zabidin Bin Salleh
Bachelor of Science (Computational Mathematics)
School of Informatics and Applied Mathematics
Hopf Bifurcation is a critical point where a system's stability switches. We investigate an
existence of Hopf Bifurcation of the system, find out the control strategy and behaviour
in the controlled model. The three objectives are to analyse the existence of Hopf
Bifurcation, to test the control strategy and behaviour of Hopf Bifurcation and to
investigate the direction and stability of bifurcating periodic solution. The existence of
Hopf Bifurcation can be prove by using two equilibrium points which are E O (0,0,0) and
E 1 (b, gb
, b) . The design a hybrid control strategy to control Hopf Bifurcation is by using
b−c
both state feedback and parameter control added to the model. Parameter φ 2 determines
the direction, parameter β 2 determines the stability while parameter τ 2 determines the
period of periodic solution. By using normal form, the direction and stability are analysed.
The numerical simulations show the effectiveness of the three methods for three
objectives.
926 | UMT UNDERGRADUATE RESEARCH DAY 2018